The LCD connection in the back of the logic board is tedious to connect and and can come off easily when putting the logic board back into place. Double check that it didn't disconnect. Another thing, sometimes the connection gets damaged by putting pressure on it in the wrong place. Be careful and also keep in mind the volume ribbon. It's very fragile and can tear if the logic board it's pulled more than it should.
I had a similar problem yesterday with an iPhone 4 screen. After i replaced the screen and turned it on, the screen e was white. You could see the apple and the apps, but the digitizer would not function. I luckily had ordered two and tested the second one and it worked perfectly. I suspected it might have to do with a damaged clip from the first installed screen. Couldn't find the problem with the white screen.